An enhanced Gibbs sampler algorithm for non-conditional simulation of Gaussian random vectors

This paper addresses the problem of simulating a Gaussian random vector with zero mean and given variance–covariance matrix, without conditioning constraints. Variants of the Gibbs sampler algorithm are presented, based on the proposal by Galli and Gao, which do not require inverting the variance–covariance matrix and therefore allow considerable time savings. Numerical experiments are performed to check the accuracy of the algorithm and to determine implementation parameters (in particular, the updating and blocking strategies) that increase the rates of convergence and mixing.